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- Title
New oscillatory instability of a confined cylinder in a flow below the vortex shedding threshold.
- Authors
Semin, B.; Decoene, A.; Hulin, J.-P.; François, M. L. M.; Auradou, H.
- Abstract
A new type of flow-induced oscillation is reported for a tethered cylinder confined inside a Hele-Shaw cell (ratio of cylinder diameter to cell aperture, $D/ h= 0. 66$) with its main axis perpendicular to the flow. This instability is studied numerically and experimentally as a function of the Reynolds number $\mathit{Re}$ and of the density ${\rho }_{s} $ of the cylinder. This confinement-induced vibration (CIV) occurs above a critical Reynolds number ${\mathit{Re}}_{c} \ensuremath{\sim} 20$ much lower than for Bénard–Von Kármán vortex shedding behind a fixed cylinder in the same configuration (${\mathit{Re}}_{\mathit{BV K}} = 111$). For low ${\rho }_{s} $ values, CIV persists up to the highest $\mathit{Re}$ value investigated ($\mathit{Re}= 130$). For denser cylinders, these oscillations end abruptly above a second value of $\mathit{Re}$ larger than ${\mathit{Re}}_{c} $ and vortex-induced vibrations (VIV) of lower amplitude appear for $\mathit{Re}\ensuremath{\sim} {\mathit{Re}}_{\mathit{BV K}} $. Close to the first threshold ${\mathit{Re}}_{c} $, the oscillation amplitude variation as $ \mathop{ (\mathit{Re}\ensuremath{-} {\mathit{Re}}_{c} )}\nolimits ^{1/ 2} $ and the lack of hysteresis demonstrate that the process is a supercritical Hopf bifurcation. Using forced oscillations, the transverse position of the cylinder is shown to satisfy a Van der Pol equation. The physical meaning of the stiffness, amplification and total mass coefficients of this equation are discussed from the variations of the pressure field.
- Subjects
MECHANICAL vibration research; FLUID-structure interaction; ENGINE cylinders -- Vibration; MATHEMATICAL models; FLUID mechanics; REYNOLDS number
- Publication
Journal of Fluid Mechanics, 2012, Vol 690, p345
- ISSN
0022-1120
- Publication type
Article
- DOI
10.1017/jfm.2011.435